Task 3: Chaos Theory Analysis
Dataset: FreshRetailNet-50K (Golden Sample)
Analysis Window: 8:00 - 22:00 (Daytime hours only)
Computed Metrics
- Hurst Exponent (H): 0.5863
(R² = 0.9497)
Interpretation: Persistent (Trending/Memory)
- Correlation Dimension (D2): 1.1452
(R² = 0.9950)
Interpretation: Fractal dimension indicating Low-dimensional Chaos or Strange Attractor degrees of freedom.
- Dimension Scan: $D_2(m)$ for $m=[2, 3, 4, 5, 6]$ (see saturation plot).
1. Time Series Dynamics
2. Phase Space Reconstruction
Visualization of the attractor in 2D embedding (x(t) vs x(t+1)).
3. Nonlinear Model Phase Portrait
Phase portrait with nullclines and vector field for the nonlinear inventory model.
4. R/S Analysis (Hurst Estimation)
Log-Log plot of Rescaled Range vs Time Scale.
5. Correlation Sum (D2 Estimation)
Log-Log plot of Correlation Integral C(r) vs Radius r.
6. Dimension Saturation Analysis
D2 vs embedding dimension; saturation indicates low-dimensional dynamics.
Generated by Systems Theory Pipeline